This invention is in the field of control systems for electric machines. Embodiments described in this specification are more specifically directed to control of alternating current (AC) electric motors operating at low speed.
Even more than a century after their introduction, AC electric motors continue to enjoy widespread deployment to this day, over a wide range of applications and sizes. AC motors have become especially popular due to their reliability and relatively low cost. Recently, modern high-speed and low-cost programmable microcontrollers have enabled complex motor control algorithms that can now control AC motors to attain increased efficiency in complex commercial, industrial, and consumer equipment and processes. For example, these control algorithms provide the ability to operate AC motors at variable speeds, which in some applications allows for the elimination of complex gears and transmissions in the driven mechanical system. These new control algorithms can also enhance the performance/cost ratio of the motor system, and increase load efficiencies, and maximize the torque per ampere performance of the motor, thus saving significant power.
Field-oriented control (“FOC”) has become a common technique in modern motor control systems. According to this approach, the stator windings of the AC motor are driven, for example by pulse-width-modulation, in such a way as to maximize the torque/ampere performance of the motor. For the case of permanent magnet rotors, FOC seeks to drive the field flux vector angle so that the rotor flux angle is 90° out of phase from the field flux, which is at the maximum torque condition.
Field-oriented control of AC motors is complicated because the rotation of the magnetic field in the stator with respect to the rotating magnetic field of the rotor can be asynchronous. As such, AC induction motor operation is characterized by a set of differential equations with time varying coefficients. The well-known “Park” transform, on which many AC motor control algorithms are based, transforms those differential equations into a set of differential equations that have time invariant coefficients. In particular, the Park transform considers motor operation according to a two-dimensional (d, q) coordinate system, where axis d is aligned with the field flux linkage component and orthogonal axis q is aligned with the torque component. By separating the field flux linkage and torque components, the motor torque can be controlled without affecting the field flux, allowing for dynamic torque control, proportional-and-integral (PI) control algorithms, and the like. Typical FOC control loops for AC motors also utilize the well-known Clarke transform to transform the three-phase time variant system of differential equations into a two coordinate time variant system, which the Park transform converts into the (d, q) coordinate system.
As fundamental in the art, closed loop control of AC motors requires knowledge of the current state of the motor, typically including the position and velocity of the rotor. Mechanical transducers, such as encoders and the like, have been used for years to sense the position and velocity of the rotor shaft in conventional electric motors. However, as is well known in the art, these sensors and associated wiring and connectors add significant cost and complexity in the motor and its control system, and are prone to inaccuracy and mechanical failure. To address these concerns, sensorless motor control techniques have been developed in the art. Sensorless induction motor control is commonly implemented by estimating the back electromagnetic force induced in the stator windings by the rotation of the rotor, from which the rotor position and velocity can be determined.
FIG. 1 illustrates a conventional controller architecture for controlling the operation of an AC motor. As well-known in the art and as discussed above, feedback control loops based on the Park transform operate according to reference signals in the direct (d) and quadrature (q) phases, shown in the example of FIG. 1 by reference currents Idref and Iqref, respectively. In the direct phase leg of the loop, error generator 2d receives direct phase reference current Idref and a feedback current Id, and forwards error signal εd corresponding to the difference of those two currents to proportional-integral (PI) controller 4d. PI controller 4d applies error signal εd to a conventional control function, which in this case is based on a sum of proportional and integral terms involving error signal εd; other control functions may alternatively be used, including PID (proportional-integral-differential) functions and the like. PI controller 4d produces direct phase control signal Vd, which is input to inverse Park transform function 6. The quadrature phase leg of this conventional control loop is similarly arranged, with error generator 2q receiving quadrature phase reference current Iqref and feedback current Iq, and forwarding error (i.e., difference) signal εq to proportional-integral (PI) controller 4q, which in turn applies a conventional control function (e.g., proportional-integral) to produce quadrature phase control signal Vq for input to inverse Park transform function 6. As conventional in the art, inverse Park transform function 6 produces spatially fixed α and β phase control signals Vα, Vβ by transforming the d and q phase control signals. Control signals Vα, Vβ are in turn applied to conventional space vector/pulse-width modulation (PWM) function 8, which produces three-phase PWM drive signals PWM(a, b, c) at the desired duty cycles and phase timing for motor phases a, b, c, respectively. Three-phase inverter 10 is a conventional power function that drives three stator windings of motor M using DC voltage Vdc, according to PWM drive signals PWM(a, b, c).
The feedback loop in this conventional architecture is based on currents in each of the stator windings, as sensed by conventional current sensors 11 and communicated as current signals Ia, Ib, Ic for the three motor phases. As shown in FIG. 1, current sensors 11 operate to estimate the back emf induced in the stator windings by the rotation of the rotor of motor M; this sensed back emf can be used to determine the position and velocity of the rotor during operation of motor M. These sensed currents Ia, Ib, Ic are typically sampled and digitized, and communicated to Clarke transform function 12 for conversion into spatially fixed α and β phase feedback signals Iα, Ib, which are applied to Park transform function 14 to produce d and q phase feedback signals Id, Iq, respectively. These feedback signals Id, Iq are applied to error generators 2d, 2q, respectively, as discussed above, closing the control loop. Accordingly, the architecture of FIG. 1 controls the operation of motor M according to the input reference currents Idref and Iqref.
Accurate estimation of rotor position and velocity requires a back emf signal of adequate magnitude and fidelity. Because back emf is proportional to rotor speed, the motor must be operating at a sufficient speed to produce a back emf having an acceptable signal-to-noise ratio. As such, conventional sensorless motor control is not well-suited for low speed control of AC motors. However, certain new AC motor applications require low speed control. For example, washing machine motors must drive an agitation cycle in which the motor operates at low RPM and reverses direction, under heavy load. Variable-speed motor control of this low-speed agitation cycle, and similar cycles, can eliminate the complex gearing and transmission that is otherwise required in modern washing machines. So-called “e-bikes”, which are bicycles that include integrated motors to assist in propulsion, provide another application in which low-speed closed loop motor control is desirable, considering that e-bike motors necessarily drive loads at relatively low speeds over significant portions of their operating time.
By way of further background, sensorless initial position detection (“IPD”) techniques are known in the art. One class of these technique uses the inherent saliency (i.e., the extent to which induction is dependent on rotor position) of the electric motor to produce a signal from which rotor position may be deduced. These conventional IPD techniques inject a high frequency carrier signal into the stator reference voltage signal. The response of the stator windings to these high frequency components, as reflected in stator feedback current, is then evaluated by a processor in the motor control system to determine the position of the rotor.
By way of further background, Kim et al., “Using Low Resolution Position Sensors in Bumpless Position/Speed Estimation Methods for Low Cost PMSM Drives”, Industry Applications Conference (IEEE, 2005), pp. 2518-24, describes a motor control architecture in which a low resolution Hall sensor arrangement measures rotor behavior at low speed acceleration, and back emf measures rotor behavior at high speed operation. The Kim et al. article also describes operating a motor according to a “crossover” function, namely a frequency-dependent weighted sum of the Hall sensor and back emf measurements, that produces estimates of rotor position and speed at intermediate frequencies between the low speed and high speed operating regimes.